In Euclidean geometry, a square is a four-sided 2D figure whose sum of inner angles is 360°. The word quadrilateral is obtained from two Latin words ‘quadri’ and ‘latus’ an interpretation four and also side respectively. Therefore, identifying the nature of quadrilateral is necessary when do the efforts to differentiate them from other polygons.

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So, what space the nature of quadrilaterals?There are two properties of quadrilaterals:

A quadrilateral must be closed form with 4 sidesAll the interior angles of a quadrilateral amount up come 360°

In this article, friend will get an idea around the 5 varieties of quadrilaterals and get to know around the nature of quadrilaterals.

This is what you’ll review in the article:

Here is a video explaining the nature of quadrilaterals:

The chart given listed below shows a square ABCD and the amount of its inner angles. All the interior angles amount up come 360°.

Thus, ∠A + ∠B + ∠C + ∠D = 360°      Properties of rhombus

A rhombus is a quadrilateral which has the complying with four properties:

Opposite angles room equalAll sides are equal and, opposite sides are parallel to each otherDiagonals bisect each various other perpendicularlySum of any two nearby angles is 180°Rhombus recipe – Area and perimeter the a rhombus

If the next of a rhombus is a then, perimeter of a rhombus = 4a

If the size of 2 diagonals of the rhombus is d1 and d2 climate the area that a rhombus = ½× d1 × d2

### Trapezium

A trapezium (called Trapezoid in the US) is a square that has only one pair the parallel sides. The parallel political parties are referred to as ‘bases’ and also the other two political parties are referred to as ‘legs’ or lateral sides.

Properties the Trapezium

A trapezium is a quadrilateral in i beg your pardon the complying with one property:

Only one pair of the contrary sides are parallel to every otherTrapezium recipe – Area and also perimeter of a trapezium

If the height of a trapezium is ‘h’(as displayed in the over diagram) then:

Perimeter of the trapezium= amount of lengths of all the political parties = abdominal muscle + BC + CD + DAArea that the trapezium =½ × (Sum of lengths the parallel sides) × h = ½ × (AB + CD) × h

These practice questions will assist you solidify the nature of trapezium

The below table summarizes all the nature of the quadrilaterals the we have actually learned so far:

 Properties the quadrilaterals Rectangle Square Parallelogram Rhombus Trapezium All Sides space equal ✖ ✔ ✖ ✔ ✖ Opposite Sides space equal ✔ ✔ ✔ ✔ ✖ Opposite Sides are parallel ✔ ✔ ✔ ✔ ✔ All angles are equal ✔ ✔ ✖ ✖ ✖ Opposite angles space equal ✔ ✔ ✔ ✔ ✖ Sum that two nearby angles is 180 ✔ ✔ ✔ ✔ ✖ Bisect each other ✔ ✔ ✔ ✔ ✖ Bisect perpendicularly ✖ ✔ ✖ ✔ ✖

The listed below table summarizes the recipe on the area and perimeter of different varieties of quadrilaterals:

 Quadrilateral formulas Rectangle Square Parallelogram Rhombus Trapezium Area l × b a² l × h ½× d1 × d2 ½× (Sum that parallel sides) × height Perimeter 2 × (l + b) 4a 2 × (l + b) 4a Sum of all the sides

Let’s exercise the applications of nature of square on the complying with sample questions:

### GMAT Quadrilaterials exercise Question 1

Adam wants to construct a fence about his rectangular garden of size 10 meters and also width 15 meters. How many meters that fence he need to buy to fence the entire garden?

20 meters25 meters30 meters40 meters50 metersSolution

Step 1: Given

Adam has actually a rectangular garden.It has a length of 10 meters and a width of 15 meters.He wants to construct a fence approximately it.

Step 2: come find

The length forced to build the fence around the whole garden.

Step 3: Approach and also Working out

The fence deserve to only it is in built approximately the exterior sides the the garden.

So, the full length that the fence required= amount of lengths of every the political parties of the garden.Since the garden is rectangular, the amount of the length of all the political parties is nothing yet the perimeter that the garden.Perimeter = 2 × (10 + 15) = 50 metres

Hence, the required length that the fence is 50 meters.

Therefore, choice E is the exactly answer.

### GMAT Quadrilaterials exercise Question 2

Steve desires to paint one rectangular-shaped wall surface of his room. The expense to paint the wall surface is \$1.5 every square meter. If the wall surface is 25 meter long and also 18 meter wide, climate what is the full cost to paint the wall?

\$ 300\$ 350\$ 450\$ 600\$ 675Solution

Step 1: Given

Steve desires to repaint one wall of his room.The wall surface is 25 meter long and 18 meters wide.Cost to paint the wall is \$1.5 every square meter.

Step 2: come find

The complete cost to paint the wall.

Step 3: Approach and Working out

A wall is painted throughout its whole area.So, if we discover the complete area of the wall surface in square meters and multiply the by the cost to paint 1 square meter the the wall then we can the full cost.Area the the wall = length × Breadth = 25 metres × 18 metres = 450 square metreTotal price to repaint the wall surface = 450 × \$1.5 = \$675

Hence, the correct answer is option E.

See more: What Does Half Mean In Math, What Do Double And Half Mean

We expect by currently you would have learned the different varieties of quadrilaterals, your properties, and formulas and also how to use these ideas to solve inquiries on quadrilaterals. The applications of quadrilateral is essential to settle geometry concerns on the GMAT. If you are planning to take it the GMAT, we can help you with high-quality study material which you can accessibility for totally free by registering here.